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Before you get started, take this readiness quiz.
In the previous section, you learned how to multiply and divide fractions. All of the examples there used either proper or improper fractions. What happens when you are asked to multiply or divide mixed numbers? Remember that we can convert a mixed number to an improper fraction . And you learned how to do that in Visualize Fractions .
Multiply:
| Convert to an improper fraction. | |
| Multiply. | |
| Look for common factors. | |
| Remove common factors. | |
| Simplify. |
Notice that we left the answer as an improper fraction, and did not convert it to a mixed number. In algebra, it is preferable to write answers as improper fractions instead of mixed numbers. This avoids any possible confusion between and
Multiply, and write your answer in simplified form:
| Convert mixed numbers to improper fractions. | |
| Multiply. | |
| Look for common factors. | |
| Remove common factors. | |
| Simplify. |
Divide, and write your answer in simplified form:
| Convert mixed numbers to improper fractions. | |
| Multiply the first fraction by the reciprocal of the second. | |
| Multiply. | |
| Look for common factors. | |
| Remove common factors. | |
| Simplify. |
Divide:
| Convert mixed numbers to improper fractions. | |
| Multiply the first fraction by the reciprocal of the second. | |
| Multiply. | |
| Look for common factors. | |
| Remove common factors. | |
| Simplify. |
The words quotient and ratio are often used to describe fractions. In Subtract Whole Numbers , we defined quotient as the result of division. The quotient of is the result you get from dividing or Let’s practice translating some phrases into algebraic expressions using these terms.
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